This multi-center prospective, randomized clinical trial will compare the radiologic procedure of transjugular intrahepatic portal-systemic shunt (TIPS) with the surgical procedure of distal splenorenal shunt (DSRS) for variceal bleeding. The health relatedness is to define the relative merits of these two treatments with respect to morbidity, mortality and cost management. The hypothesis to be tested is that TIPS will have a significantly higher rebleeding rate and incidence of encephalopathy than DSRS. Uncontrolled studies show a variceal rebleeding rate of 20 percent after TIPS compared to 5 percent after DSRS, and an encephalopathy incidence of 30 percent after TIPS compared to 14 percent after DSRS. In this study, Childs Class A and B Cirrhotic patients with variceal bleeding which cannot be managed by endoscopy will be randomized to TIPS or DSRS.